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A125558 Central column of triangle A090181. 5
1, 1, 6, 50, 490, 5292, 60984, 736164, 9202050, 118195220, 1551580888, 20734762776, 281248448936, 3863302870000, 53644719852000, 751920156592200, 10626401036545650, 151269944167296900, 2167317913508055000 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

[1,6,50,490,5292,...] is a column in triangle of Narayana numbers A001263.

Number of Dyck 2n-paths with exactly n peaks. - Peter Luschny, May 10 2014

LINKS

Harvey P. Dale, Table of n, a(n) for n = 0..800

FORMULA

a(0)=1, a(n) = Catalan(n)^2*(n+1)/2 = A000108(n)^2*(n+1)/2 for n>0.

a(n) = A090181(2*n, n).

G.f.: 1 + x*3F2( (1, 3/2, 3/2); (2, 3))(16 x) = 1 + (2F1( (1/2, 1/2); {2})(16*x) - 1)/2. - Olivier Gérard, Feb 16 2011

MAPLE

seq(ceil(1/2*(n+1)*((binomial(2*n, n)/(1+n))^2)), n=0..18); # Zerinvary Lajos, Jun 18 2007

MATHEMATICA

CoefficientList[

Series[1 + (HypergeometricPFQ[{1/2, 1/2}, {2}, 16 x] - 1)/(2), {x, 0,

    20}], x]

Join[{1}, Table[CatalanNumber[n]^2 (n+1)/2, {n, 20}]] (* Harvey P. Dale, Oct 19 2011 *)

CROSSREFS

Equals A000888(n)/2 for n>0.

Cf. A090181.

Sequence in context: A039742 A243667 A303562 * A005416 A300989 A105617

Adjacent sequences:  A125555 A125556 A125557 * A125559 A125560 A125561

KEYWORD

easy,nonn

AUTHOR

Philippe Deléham, Jan 01 2007, Oct 11 2007

STATUS

approved

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Last modified January 17 10:20 EST 2021. Contains 340214 sequences. (Running on oeis4.)